Discrete random variables and probability distributions, expected value, variance and standard deviation, fair games and insurance.
Random variables
Flip three coins and count the heads. The result is a number, but you don't know which until you flip. A random variable assigns a number to each outcome of a random experiment.
Expected value
It's the long-run average if the experiment were repeated many times. It doesn't have to be a possible value.
Fair games and insurance
A game is fair if the expected net gain is \(0\).
Variance and standard deviation
Practice
Quick check
What is the expected value of one roll of a fair die?
\(\frac{1 + 2 + 3 + 4 + 5 + 6}{6} = 3.5\).
Quick check
A game is called fair when:
On average, neither player gains or loses.
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